{"paper":{"title":"Recovering functions from the modulation spaces $\\mathscr{F}W$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Jeff Ledford","submitted_at":"2015-01-10T05:08:48Z","abstract_excerpt":"In this short note we show that functions in the modulation space $\\mathscr{F}W=\\{ f: \\sum_{j\\in\\mathbb{Z}^n}\\| \\hat{f}(\\cdot+2\\pi j)\\|_{L_\\infty([-\\pi,\\pi]^n)}<\\infty \\}$ enjoy similar recovery properties as band-limited functions. If $\\{\\phi_\\alpha\\}$ is a regular family of cardinal interpolators, then one can build an approximand of $f$ using the fundamental functions corresponding to $\\phi_\\alpha$. Then taking the appropriate limit, one recovers $f$ both in norm and pointwise."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02312","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}